Normalized eigenvectors for nonlinear abstract and elliptic operators

DOI10.1006/jdeq.1998.3592zbMath0931.47050OpenAlexW1976726264MaRDI QIDQ1300101

Athanassios G. Kartsatos, Igor V. Skrypnik

Publication date: 23 February 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3592

zbMATH Keywords

eigenvalue problemelliptic boundary value problems\(m\)-accretivemaximal monotoneexistence of eigenvectorsnormalization conditionstype \((S)_+\)

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Nonlinear elliptic equations (35J60) Degree theory for nonlinear operators (47H11) General theory of partial differential operators (47F05) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

Related Items (15)

On the normalized eigenvalue problems for nonlinear elliptic operators. II ⋮ Eigenvalue results for pseudomonotone perturbations of maximal monotone operators ⋮ On the normalized eigenvalue problems for nonlinear elliptic operators ⋮ Implicit eigenvalue problems for maximal monotone operators ⋮ Some eigenvalue results for perturbations of maximal monotone operators ⋮ Some eigenvalue results for maximal monotone operators ⋮ Topological degree theories and nonlinear operator equations in Banach spaces ⋮ A new topological degree theory for densely defined \((S_+)_L\)-perturbations of multivalued maximal monotone operators in reflexive separable Banach spaces ⋮ The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces ⋮ Eigenvalues of quasibounded maximal monotone operators ⋮ On the approximate \(K\)-controllability of nonlinear systems in Banach spaces ⋮ The index of a critical point for densely defined operators of type (𝑆₊)_{𝐿} in Banach spaces ⋮ Invariance of domain and eigenvalues for perturbations of densely defined linear maximal monotone operators ⋮ The Leray-Schauder approach to the degree theory for \((S_+)\)-perturbations of maximal monotone operators in separable reflexive Banach spaces ⋮ On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces

Cites Work

• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in banach spaces
• New results in the perturbation theory of maximal monotone and $M$-accretive operators in Banach spaces
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